For the numerical simulation of Navier-Stokes equations, the choice of the mesh type plays a significant role. Comparative calculations on different mesh types illustrates that the best simulation precision, characterized by minimum Local Truncation Error (LTE), is obtained on Cartesian meshes. For the boundary representation the Immersed Boundary (IB) approach, which does not require a boundary-conforming mesh, is used. Use of Cartesian meshes together with Immersed Boundary approach makes it possible to efficiently: minimize approximation errors; build operators with good spectral properties, so that robustness of method is guaranteed; speed up the process of grid generation; and make grid generation robust and flexible. Many other CFD methods require a mesh that fits the boundaries of the computational domain and often complex internal geometries. The body-fitted grid generation used is time-consuming, often requiring manual intervention to modify and cleaning-up the CAD geometry as a pre-requisite.
To implement the IB approach efficiently in FloEFD, a number of issues needed to be resolved: approximation of the governing equations in cut-cells that contain the solid-fluid interface; capture of boundary layers effects irrespective of boundary layer thickness using a Two-Scale Wall Functions (2SWF) approach (see Mentor Graphics Corp., 2011); automatic mesh generation with automatic detection of initial mesh settings (octree-based mesh structure); and Solution Adaptive Refinement (SAR).
Test cases given in this paper represent a small selection of our validation examples that illustrate the IB approach precision and flexibility of FloEFD meshing technology in the wide range of industrial examples of geometry and physical formulations.